Python | Check if list is strictly increasing

The test for a monotonic sequence is a utility that has manifold applications in mathematics and hence every sphere related to mathematics. As mathematics and Computer Science generally go parallel, mathematical operations such as checking for strictly increasing sequence can be useful to gather knowledge. The same argument can be extended for strictly decreasing lists also. Lets discuss certain ways to perform this test. 

Method #1 : Using all() + zip() The all() generally checks for all the elements fed to it. The task of zip() is to link list beginning from the beginning and list beginning from the first element, so that a check can be performed on all elements. 

Python3

# Python3 code to demonstrate
# to check for strictly increasing list
# using zip() + all()

# initializing list
test_list = [1, 4, 5, 7, 8, 10]

# printing original lists
print ("Original list : " + str(test_list))

# using zip() + all()
# to check for strictly increasing list
res = all(i < j for i, j in zip(test_list, test_list[1:]))

# printing result
print ("Is list strictly increasing ? : " + str(res))

Output:

Original list : [1, 4, 5, 7, 8, 10]
Is list strictly increasing ? : True

Method #2 : Using reduce() + lambda reduce() coupled with lambda can also perform this task of checking for monotonicity. reduce function is used to cumulate the result as True or False, lambda function checks for each index value with next index value. 

Python3

# Python3 code to demonstrate
# to check for strictly increasing list
# using reduce() + lambda

# initializing list
test_list = [1, 4, 5, 7, 8, 10]

# printing original lists
print ("Original list : " + str(test_list))

# using reduce() + lambda
# to check for strictly increasing list
res = bool(lambda test_list: reduce(lambda i, j: j if
                 i < j else 9999, test_list) != 9999)

# printing result
print ("Is list strictly increasing ? : " + str(res))

Output:

Original list : [1, 4, 5, 7, 8, 10]
Is list strictly increasing ? : True

Method #3: Using itertools.starmap() + zip() + all() Yet another method to perform this task, starmap() works in binding the operation with the zipped lists as done in method 1, and all() also performs a similar task of cumulation of result. 

Python3

# Python3 code to demonstrate
# to check for strictly increasing list
# using itertools.starmap() + zip() + all()
import operator
import itertools

# initializing list
test_list = [1, 4, 5, 7, 8, 10]

# printing original lists
print ("Original list : " + str(test_list))

# using itertools.starmap() + zip() + all()
# to check for strictly increasing list
res = all(itertools.starmap(operator.le,
         zip(test_list, test_list[1:])))

# printing result
print ("Is list strictly increasing ? : " + str(res))

Output:

Original list : [1, 4, 5, 7, 8, 10]
Is list strictly increasing ? : True

Method #4 : Using sort() and extend() methods

Python3

# Python3 code to demonstrate
# to check for strictly increasing list

# initializing list
test_list = [1, 4, 5, 7, 4, 10]

# printing original lists
print ("Original list : " + str(test_list))

# to check for strictly increasing list
res=False
x=[]
x.extend(test_list)
test_list.sort()
if(x==test_list):
    res=True
# printing result
print ("Is list strictly increasing ? : " + str(res))

Output

Original list : [1, 4, 5, 7, 4, 10]
Is list strictly increasing ? : False

Method #5 : Using stack approach:

One approach to check if a list is strictly increasing is to use a stack data structure. A stack is a Last In, First Out (LIFO) data structure, meaning that the last element added to the stack is the first one to be removed.

Here’s an example of using a stack to check if a list is strictly increasing:

Python3

def is_strictly_increasing(lst):
    stack = []
    for i in lst:
        if stack and i <= stack[-1]:
            return False
        stack.append(i)
    return True

test_list = [1, 4, 5, 7, 8, 10]
print(is_strictly_increasing(test_list))  # True

test_list = [1, 4, 5, 7, 7, 10]
print(is_strictly_increasing(test_list))  # False
#This code is contributed by Edula Vinay Kumar Reddy

Output

True
False

The time complexity of this approach is O(n), as the list is traversed once. The space complexity is also O(n), as the stack may store up to n elements at a time.